Related papers: Stable Canonical Rules for Intuitionistic Modal Lo…
We develop foundational aspects of stability theory in affine logic. On the one hand, we prove appropriate affine versions of many classical results, including definability of types, existence of non-forking extensions, and other…
The computational properties of modal and propositional dependence logics have been extensively studied over the past few years, starting from a result by Sevenster showing NEXPTIME-completeness of the satisfiability problem for modal…
The use of exponentials in linear logic greatly enhances its expressive power. In this paper we focus on nonassociative noncommutative multiplicative linear logic, and systematically explore modal axioms K, T, and 4 as well as the…
Stability is required for real world controlled systems as it ensures that those systems can tolerate small, real world perturbations around their desired operating states. This paper shows how stability for continuous systems modeled by…
Intuitionistic conditional logic, studied by Weiss, Ciardelli and Liu, and Olkhovikov, aims at providing a constructive analysis of conditional reasoning. In this framework, the would and the might conditional operators are no longer…
The intuitionistic modal logics considered between Constructive K (CK) and Intuitionistic K (IK) differ in their treatment of the possibility (diamond) connective. It was recently rediscovered that some logics between CK and IK also…
Continuous Markovian Logic (CML) is a multimodal logic that expresses quantitative and qualitative properties of continuous-time labelled Markov processes with arbitrary (analytic) state-spaces, henceforth called continuous Markov processes…
We introduce a modal logic for describing statistical knowledge, which we call statistical epistemic logic. We propose a Kripke model dealing with probability distributions and stochastic assignments, and show a stochastic semantics for the…
In this paper we investigate certain systems of propositional intuitionistic modal logic defined semantically in terms of neighborhood structures. We discuss various restrictions imposed on those frames but our constant approach is to…
Informal logic is a method of argument analysis which is complementary to that of formal logic, providing for the pragmatic treatment of features of argumentation which cannot be reduced to logical form. The central claim of this paper is…
This paper introduces a fundamental result, which is relevant for Answer Set programming, and planning. For the first time since the definition of the stable model semantics, the class of logic programs for which a stable model exists is…
Randomly-assembled dynamical systems are theoretically predicted to be unstable upon crossing a critical threshold of complexity, as first shown by May. Yet, empirical complex systems exhibit remarkable stability, indicating the presence of…
Three classes of models of QHC, the joint logic of problems and propositions, are constructed, including a class of subset/sheaf-valued models that is related to solutions of some actual problems (such as solutions of algebraic equations).…
In this paper we investigate the links between instantiated argumentation systems and the axioms for non-monotonic reasoning described in [9] with the aim of characterising the nature of argument based reasoning. In doing so, we consider…
This paper introduces a natural deduction calculus for intuitionistic logic of belief $\mathsf{IEL}^{-}$ which is easily turned into a modal $\lambda$-calculus giving a computational semantics for deductions in $\mathsf{IEL}^{-}$. By using…
Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under…
We present a logical system that combines the well-known classical epistemic concepts of belief and knowledge with a concept of evidence such that the intuitive principle \textit{`evidence yields belief and knowledge'} is satisfied. Our…
The multi-valued logic of {\L}ukasiewicz is a substructural logic that has been widely studied and has many interesting properties. It is classical, in the sense that it admits the axiom schema of double negation, [DNE]. However, our…
We investigate the set-theoretic strength of several maximality principles that play an important role in the study of modal and intuitionistic logics. We focus on the well-known Fine and Esakia maximality principles, present two…
Building on previous work by Andr\'e Platzer, we present a formal language for Stochastic Differential Dynamic Logic, and define its semantics, axioms and inference rules. Compared to the previous effort, our account of the Stochastic…